Literature / What is the Name of This Book?

What Is the Name of This Book? The Riddle of Dracula and Other Logical Puzzles is a 1978 book by mathematician Raymond Smullyan.

It had two follow-ups in 1982: The Lady or the Tiger? (not to be confused with the original short story by Frank Stockton that the title references) and Alice in Puzzle-Land, referencing, of course, Lewis Carroll's Alice in Wonderland).

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Tropes in What Is the Name of This Book?:

• Engagement Challenge: Portia offers engagement challenges based on logic puzzles, as do her daughter, granddaughter, and distant descendant, all named Portia.
• Generation Xerox:
  • Portia's daughter Portia II, her granddaughter Portia III, and her descendant Portia N test the intelligence of their suitors by logic puzzles whose objective is to determine which one of several caskets contains an object, just like the original Portia. Though the puzzles get progressively harder.
  • Casket-makers Bellini and Cellini — who only inscribed their caskets with true and false statements, respectively, — had sons who were also casket-makers and abided by the same rules.
• Historical Domain Character: Giovanni Bellini and Benvenuto Cellini were an Italian Renaissance artist and sculptor, respectively. However, Bellini died only 16 years after Cellini was born, and neither of them actually made caskets with logic puzzles. Probably.
• I Know You Know I Know: Appears in chapter 13.
  "Here is how I reasoned: I know my wife likes cake and I know she knows that I like cake. I also know she loves me and wants me to be happy, therefore she would want me to have the larger piece. Therefore I took the larger piece."
• Knights and Knaves: Many, many variations on the setup, usually making statements about themselves or each other.
• Liar's Paradox: Many puzzles rely on the fact that it is logically impossible for someone known to either always speak the truth under given conditions, or to always lie under given conditions, to say "I'm lying" or anything else to that effect (such as "I'm a knave", where a knave is defined as a person who always lies).
• Logic Bomb: The first two stories in the book are anecdotes told by Smullyan himself.
  • In the first story, six-year-old Raymond's brother Emile told Raymond that he was going to fool him, and then didn't — thus fooling him by subverting his expectation that he'd fool him.
  • The other anecdote tells about a job interview where Smullyan was asked, "Do you object to telling a little lie every now and again?" At the time, he did object to that, but, wanting to get the job, he falsely claimed "No". But since he did it, it meant that he didn't actually object to occasionally telling lies, which meant that his "No" was a true statement, even though he felt like he was lying...
  • For a fictional case, see "Shaggy Dog" Story below.
• Our Vampires Are Different: This book's version of Transylvania is populated by humans, who always say what they believe is true, and vampires, who always say what they believe is false. In addition, both humans and vampires can be insane, believing in falsehoods.
  • This leads to an interesting variation of the Liar's Paradox, since while they still can't say "I'm lying", they can say "I'm a vampire" or "I'm insane". More interestingly, saying "I'm a vampire" tells you nothing about whether they're actually a vampire, but only someone insane can say it; similarly, only a vampire can say "I am insane". Saying "I am sane" means the speaker is human, saying "I am a human" means the speaker is sane. This is the key to solving many of the Transylvania puzzles.
• Public Domain Character:
  • One chapter uses characters from Alice's Adventures in Wonderland and Through the Looking-Glass.
  • Portia from Shakespeare's The Merchant of Venice.
  • Dracula.
• "Shaggy Dog" Story: Chapter 11 tells about a philosopher's journey to find the high priests of the Temple of Baal, who are rumored to know the answer to the question "Why is there something instead of nothing?" After passing many challenges in the form of logic puzzles, he finally finds a high priest who knows the answer, and asks him the question. Said high priest is a knave, meaning he always lies. When the philosopher asks him "Why is there something instead of nothing?", he replies, "There is something instead of nothing." Since he lied, it means that nothing actually exists; but since, by the tale's premise, the priest, the philosopher, and the Island of Baal do exist, this renders the tale logically impossible.
  Narrator: The curious thing is that up until the last story (prob­lem 157), everything I told you, no matter how implausible it may have seemed, was logically possible. But when I told you the last story, that was the straw that broke the camel's back!
• Troll:
  • After Alice learns everything there is to know about Tweedledum and Tweedledee — specifically, which is which, which one of them lies on which days of the week, and which one actually owns the rattle that caused their feud — Humpty Dumpty casts everything she knows into doubt by revealing that they have a secret third brother, Tweedledoo, who occasionally visits them and who always lies. Jabberwocky then tells the narrator four tales about Alice's further encounters with the brothers. Turns out that three of them are false, and in the remaining true one, Alice can deduce that Tweedledoo doesn't actually exist. Humpty Dumpty lied to her just to mess with her.
  • The brothers themselves have shades of this. In one puzzle, on a day where they both tell the truth, one says, "If I'm Tweedledum then he's Tweedledee", and the other says, "If he's Tweedledee then I'm Tweedledum". Both statements are trivially true and don't give Alice any new information.